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JEE Main & Advanced Mathematics Vector Algebra Question Bank Modulus of vector Algebra of vectors

  • question_answer
    The point having position vectors \[2\mathbf{i}+3\mathbf{j}+4\mathbf{k},\,\,\]\[3\mathbf{i}+4\mathbf{j}+2\mathbf{k},\] \[4\mathbf{i}+2\mathbf{j}+3\mathbf{k}\] are the vertices of                                                                                                                        [EAMCET 1988]

    A) Right angled triangle            

    B) Isosceles triangle

    C) Equilateral triangle               

    D) Collinear

    Correct Answer: C

    Solution :

    Here,\[\overrightarrow{OA}=2\mathbf{i}+3\mathbf{j}+4\mathbf{k},\] \[\overrightarrow{OB}=3\mathbf{i}+4\mathbf{j}+2\mathbf{k}\] \[\overrightarrow{OC}=4\mathbf{i}+2\mathbf{j}+3\mathbf{k}\] So, \[\overrightarrow{AB}=\mathbf{i}+\mathbf{j}-2\mathbf{k},\] \[\overrightarrow{BC}=\mathbf{i}-2\mathbf{j}+\mathbf{k}\], \[\overrightarrow{CA}=2\mathbf{i}-\mathbf{j}-\mathbf{k}\] Clearly \[|AB|\,=\,|BC|\,=\,|CA|\,=\sqrt{6}\] So these points are vertices of an equilateral triangle.


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